The majority of methods for the design of Phase I trials for in oncology are intended for studies involving a single cytotoxic agent. The goal of these studies is to estimate the 'maximally tolerated dose', the highest dose that can be administered with an acceptable level of toxicity. A key assumption of these methods is the monotonicity of the dose- response curve. In this case, the dose-response curve is said to follow a 'simple order' because the ordering of the probabilities of a 'dose-limiting toxicity' (DLT) for any pair of doses is known; administration of greater doses of the agent can be expected to produce DLT's in increasing proportions of patients. It is becoming increasingly common for combinations of agents to be tested in phase I trials. In these studies, the probabilities of a DLT associated with the dose combinations often follow a 'partial order' in that there are pairs of dose combinations for which the ordering of the probabilities is not known. This proposal uses Bayesian methods, combining features of the continual reassessment method and order restricted inference to develop designs for phase I trials in which the probabilities follow a partial order. In addition, we will adapt our methods for cycle-specific toxicities. Finally, we will develop internet-accessible software to assist users in designing and carrying out partially ordered phase I trials. Even though our emphasis is on phase I trials of combinations, the methods we develop can shed light on other issues in phase I trial design, including the study of ordered groups and trials of cancer vaccines.